DOCSLIB.ORG

Fluid/Solid Boundary Conditions in Non-Isothermal Systems

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Fluid/Solid Boundary Conditions in Non-Isothermal Systems Fluid/Solid Boundary Conditions in Non-Isothermal Systems Ph DANIEL E. ROSNER NASA Grant No. NAG 3-1951 Yale University, Department of Chemical Engineering High Temperature Chemical Reaction Engineering (HTCRE-) Laboratory New Haven, CT 06520-8286 USA 1. Introduction, background and objectives In a short paper (Phys. Fluids A 1 (11) 1761-1763 (1989)) the PI pointed out for the first time that vapor-filled nonisothermal ampoules operating in micro-gravity will experience convection driven by both "wall-induced thermal creep"* as well as thermal stresses (in the bulk vapor). But, as emphasized in our subsequent review of thermally-induced particle phoresis (Rosner et.aL, 1992) these "thermal creep" boundary condition (BC-) phenomena also determine the readily observed migration rates ("phoresis") of suspended "small" solid particles in suspension. This led us to the idea that careful phoresis measurements in a suitably designed microgravity environment (to preclude complications such as 'sedimentation' for particles large enough both to sustain large temperature differences and avoid appreciable Brownian motion) could be used to obtain unambiguous information about the nature of the tangential momentum transfer boundary condition over a broad range of Newtonian fluid densities. This would be especially interesting since present theoretical methods are really valid only in the low density ("ideal"-) gas limit. As noted below, we recently carried out numerical simulations of the "low-density" Boltzmann equation which not only clarified the wall ("creep") BC, but also thermal stress (non-Newton-Stokes-) effects within such crystal- growth ampoule flows. However, to clarify the nature of the BC transition from the Enskog- Chapman regime to the technologically important but theoretically less tractable case of liquid- like densities (including supercritical polyatomic vapors) it is inevitable that high-quality experimental data for carefully selected fluid/solid interfaces will be required. The best environment for obtaining these data appears to be the microgravity environment, as spelled out in Section 2 below. Previous theoretical work on "thermal creep" at fluid/solid interfaces (going back to J.C. Maxwell[1879]) has been understandably focused on "structureless", single component low density gas motion adjacent to a non-isothermal smooth flat solid surface, usually exploiting an approximate (eg. linearized) model of the Boltzmann equation and a "diffuse reflection" molecule/surface interaction model. However, since many applications are multi-dimensional and involve non-dilute mixtures of disparate mass polyatomic molecules, frequently well outside of the domain of "ideal" gas behavior, many generalizations are urgently needed to understand and ultimately predict such flows, whether in micro-gravity or in ground-based laboratories. Progress will be slow in the absence of reliable experimental data on the 591 dimensionlessthermal creep (or wall 'slip') coefficient, Ctc , appearing in the relevant tangential momentum BC: (Vt,w)tc =Ctc'n'(°lnTnuid,w/'X) ( 1 ) Here (vt, w )tc is the thermal creep contribution to the tangential component (x-direction) of the *It is rather remarkable that, despite the small Knudsen numbers typically associated with these flows, one cannot apply "no-slip" boundary conditions along the non-isothermal ampoule walls-ie, the walls drive a significant amount of convection ! fluid velocity relative to the solid surface, n is the momentum diffusivity ("kinematic viscosity", m/r ) of the fluid, and Tfluid, w is the fluid temperature evaluated at the fluid/solid interface. One sees from Eq.(1) that such wall-induced creep flow is subtle since for solids in gases, if Ctc =O(1) (as appears to be the case from the limited available experiments) then the Mach number associated with the wall creep flow is of the same order of magnitude as the fractional change of gas temperature over one mean-free-path. In our view, the ultimate goal of this line of research is a rational molecular level theory which predicts the dependence of Ctc on relevant dimensionless parameters describing the way fluid molecules interact with the solid surface, and how they interact among themselves (see, eg., Rosner and Papadopoulos,1996). Accordingly, microgravity-based experimental data (Section 2 below) will be an important step forward. 2. Photophoretic "space race" experiments It might be thought that the best way to experimentally obtain this rather important dimensionless coefficient would be the "direct" one of measuring fluid velocities near non- isothermal solid surfaces using, say, laser velocimetry on very small (negligible inertia) particles immersed in the local fluid. However, even if the microgravity environment were used to preclude any confusion from bouyancy-driven convection, the phenomenon of thermo- phoresis (eg., Rosner et.al., 1992, Gomez and Rosner,1993) would inevitably cause the local motion of small "tracer" particles to depart systematically from that of the non-isothermal host fluid! To avoid this dilemma we suggest exploiting the closely related phenomenon of photophoresis under microgravity conditions. This phenomenon (in which the intraparticle temperature nonuniformity which causes the thermal creep in the surrounding fluid is induced by the absorption of incident radiation) is quite sensitive to the momentum transfer boundary condition of interest (Eq.(1)) and becomes rather important at particle sizes at which sedimentation phenomena would normally set in for ground-based experiments (Castillo et.al.,1990, Mackowski 1989,1990). Thus, microgravity experiments involving deliberately suspended supermicron spherical solid particles of low thermal conductivity but with known "optical" properties (over a wide range of transparent fluid densities) could prove to be 592 extremely valuable in defining the nature of the momentumtransfer boundary condition "transition" (ie.,Ctc-trends)from thelow density(idealgas-)limit to the bona-fide "liquid" limit. One simple realization of this basic idea, would, in effect, be a "space-race" of illuminated, absorbing spheres, each immersed and simultaneously released in a different pure, transparent Newtonian fluid (including dense as well as low density polyatomic gases, and certain transparent Newtonian liquids). These low thermal conductivity spheres would be illuminated by a common non-polarized, omni-directional radiation source, and each would be large enough to sustain a significant temperature difference across its diameter (despite the isothermal environment far from each sphere). Moreover, as mentioned above, in the microgravity environment 'sedimentation' or 'bouyant rise' would be eliminated as a complication, broadening considerably the choice of informative fluid/solid combinations. Therefore, from the "photo-phoretic" drift velocity of these spheres, (recorded "from above" via a TV camera ) and the relevant theory (see, eg., Rosner et.al.,1992, and Mackowski, 1989), it should be possible to extract the tangential momentum thermal creep coefficient , Ctc , operative at each fluid/solid interface. We have already identified most of the basic requirements for such experiments t(o extract the dimensionless thermal creep coefficient, Ctc, from measurements of photophoretic drift velocities in different Newtonian fluids). Indeed, we are currently evaluating the possible construction/use of composite test spheres to amplify the effects sought---ie., opaque thin shells containing a thermally insulating rigid "core" of small mass. As a part of this research program we are currently working out the (asymptotic) theory of photophoresis for such test-spheres. 3. Thermophoresis of isolated solid spheres and aggregates in gases A little-noticed but potentially very important feature (see below) of the existing theory of solid sphere thermophoresis in ideal gases is that for sphere thermal conductivities less than about 2.3 times that of the background gas, the sphere thermophoretic diffusivity can actually exceed that in the free-molecule limit! This remarkable feature, which translates to larger spheres moving faster than their smaller counterparts, may be partially 'rationalized' by noticing that, whereas the (Waldmann-) free-molecule limit calculation (see,eg., Rosner,1980, Garcia-Ybarra and Rosner,1989, or Loyalka,1992) does not involve either the abovementioned creep coefficient, or the sphere thermal conductivity, the near-continuum value does contain both Ctc, and sphere thermal conductivity. We mention this behavior here because, in related studies, we have been clarifiying the effects of intrinsic thermal conductivity, particle morphology, and Knudsen number on the thermophoretic properties of suspended particles (in ideal gases), and 'coagulation-aged' populations thereof (Rosner and Khalil, 1998). While a comprehensive theory for aggregate thermophoresis as a function of Knudsen number is not yet available (see,eg., Rosner et.al.,1991), and outside the scope of the present program, we have proposed that a rational estimate can be obtained by imagining that an aggregate behaves like a homogeneous sphere with an effective mobility diameter about equal to the gyration diameter but with an effective thermal conductivity equal to that expected for the 'granular medium' (of spherules) existing at the gyration radius (for some details, see Tandon and Rosner, 1995). Results of this plausible model indicate that the thermophoretic transport rates of aggregates of even
Load more

Recommended publications
  • Equation of State for the Lennard-Jones Fluid
    Equation of State for the Lennard-Jones Fluid Monika Thol1*, Gabor Rutkai2, Andreas Köster2, Rolf Lustig3, Roland Span1, Jadran Vrabec2 1Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany 2Lehrstuhl für Thermodynamik und Energietechnik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany 3Department of Chemical and Biomedical Engineering, Cleveland State University, Cleveland, Ohio 44115, USA Abstract An empirical equation of state correlation is proposed for the Lennard-Jones model fluid. The equation in terms of the Helmholtz energy is based on a large molecular simulation data set and thermal virial coefficients. The underlying data set consists of directly simulated residual Helmholtz energy derivatives with respect to temperature and density in the canonical ensemble. Using these data introduces a new methodology for developing equations of state from molecular simulation data. The correlation is valid for temperatures 0.5 < T/Tc < 7 and pressures up to p/pc = 500. Extensive comparisons to simulation data from the literature are made. The accuracy and extrapolation behavior is better than for existing equations of state. Key words: equation of state, Helmholtz energy, Lennard-Jones model fluid, molecular simulation, thermodynamic properties _____________ *E-mail: [email protected] Content Content ....................................................................................................................................... 2 List of Tables .............................................................................................................................
    [Show full text]
  • 1 Fluid Flow Outline Fundamentals of Rheology
    Fluid Flow Outline • Fundamentals and applications of rheology • Shear stress and shear rate • Viscosity and types of viscometers • Rheological classification of fluids • Apparent viscosity • Effect of temperature on viscosity • Reynolds number and types of flow • Flow in a pipe • Volumetric and mass flow rate • Friction factor (in straight pipe), friction coefficient (for fittings, expansion, contraction), pressure drop, energy loss • Pumping requirements (overcoming friction, potential energy, kinetic energy, pressure energy differences) 2 Fundamentals of Rheology • Rheology is the science of deformation and flow – The forces involved could be tensile, compressive, shear or bulk (uniform external pressure) • Food rheology is the material science of food – This can involve fluid or semi-solid foods • A rheometer is used to determine rheological properties (how a material flows under different conditions) – Viscometers are a sub-set of rheometers 3 1 Applications of Rheology • Process engineering calculations – Pumping requirements, extrusion, mixing, heat transfer, homogenization, spray coating • Determination of ingredient functionality – Consistency, stickiness etc. • Quality control of ingredients or final product – By measurement of viscosity, compressive strength etc. • Determination of shelf life – By determining changes in texture • Correlations to sensory tests – Mouthfeel 4 Stress and Strain • Stress: Force per unit area (Units: N/m2 or Pa) • Strain: (Change in dimension)/(Original dimension) (Units: None) • Strain rate: Rate
    [Show full text]
  • Chapter 3 Equations of State
    Chapter 3 Equations of State The simplest way to derive the Helmholtz function of a fluid is to directly integrate the equation of state with respect to volume (Sadus, 1992a, 1994). An equation of state can be applied to either vapour-liquid or supercritical phenomena without any conceptual difficulties. Therefore, in addition to liquid-liquid and vapour -liquid properties, it is also possible to determine transitions between these phenomena from the same inputs. All of the physical properties of the fluid except ideal gas are also simultaneously calculated. Many equations of state have been proposed in the literature with either an empirical, semi- empirical or theoretical basis. Comprehensive reviews can be found in the works of Martin (1979), Gubbins (1983), Anderko (1990), Sandler (1994), Economou and Donohue (1996), Wei and Sadus (2000) and Sengers et al. (2000). The van der Waals equation of state (1873) was the first equation to predict vapour-liquid coexistence. Later, the Redlich-Kwong equation of state (Redlich and Kwong, 1949) improved the accuracy of the van der Waals equation by proposing a temperature dependence for the attractive term. Soave (1972) and Peng and Robinson (1976) proposed additional modifications of the Redlich-Kwong equation to more accurately predict the vapour pressure, liquid density, and equilibria ratios. Guggenheim (1965) and Carnahan and Starling (1969) modified the repulsive term of van der Waals equation of state and obtained more accurate expressions for hard sphere systems. Christoforakos and Franck (1986) modified both the attractive and repulsive terms of van der Waals equation of state. Boublik (1981) extended the Carnahan-Starling hard sphere term to obtain an accurate equation for hard convex geometries.
    [Show full text]
  • Two-Way Fluid–Solid Interaction Analysis for a Horizontal Axis Marine Current Turbine with LES
    water Article Two-Way Fluid–Solid Interaction Analysis for a Horizontal Axis Marine Current Turbine with LES Jintong Gu 1,2, Fulin Cai 1,*, Norbert Müller 2, Yuquan Zhang 3 and Huixiang Chen 2,4 1 College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China; [email protected] 2 Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA; [email protected] (N.M.); [email protected] (H.C.) 3 College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China; [email protected] 4 College of Agricultural Engineering, Hohai University, Nanjing 210098, China * Correspondence: fl[email protected]; Tel.: +86-139-5195-1792 Received: 2 September 2019; Accepted: 23 December 2019; Published: 27 December 2019 Abstract: Operating in the harsh marine environment, fluctuating loads due to the surrounding turbulence are important for fatigue analysis of marine current turbines (MCTs). The large eddy simulation (LES) method was implemented to analyze the two-way fluid–solid interaction (FSI) for an MCT. The objective was to afford insights into the hydrodynamics near the rotor and in the wake, the deformation of rotor blades, and the interaction between the solid and fluid field. The numerical fluid simulation results showed good agreement with the experimental data and the influence of the support on the power coefficient and blade vibration. The impact of the blade displacement on the MCT performance was quantitatively analyzed. Besides the root, the highest stress was located near the middle of the blade. The findings can inform the design of MCTs for enhancing robustness and survivability.
    [Show full text]
  • Navier-Stokes Equations Some Background
    Navier-Stokes Equations Some background: Claude-Louis Navier was a French engineer and physicist who specialized in mechanics Navier formulated the general theory of elasticity in a mathematically usable form (1821), making it available to the field of construction with sufficient accuracy for the first time. In 1819 he succeeded in determining the zero line of mechanical stress, finally correcting Galileo Galilei's incorrect results, and in 1826 he established the elastic modulus as a property of materials independent of the second moment of area. Navier is therefore often considered to be the founder of modern structural analysis. His major contribution however remains the Navier–Stokes equations (1822), central to fluid mechanics. His name is one of the 72 names inscribed on the Eiffel Tower Sir George Gabriel Stokes was an Irish physicist and mathematician. Born in Ireland, Stokes spent all of his career at the University of Cambridge, where he served as Lucasian Professor of Mathematics from 1849 until his death in 1903. In physics, Stokes made seminal contributions to fluid dynamics (including the Navier–Stokes equations) and to physical optics. In mathematics he formulated the first version of what is now known as Stokes's theorem and contributed to the theory of asymptotic expansions. He served as secretary, then president, of the Royal Society of London The stokes, a unit of kinematic viscosity, is named after him. Navier Stokes Equation: the simplest form, where is the fluid velocity vector, is the fluid pressure, and is the fluid density, is the kinematic viscosity, and ∇2 is the Laplacian operator.
    [Show full text]
  • Ductile Deformation - Concepts of Finite Strain
    327 Ductile deformation - Concepts of finite strain Deformation includes any process that results in a change in shape, size or location of a body. A solid body subjected to external forces tends to move or change its displacement. These displacements can involve four distinct component patterns: - 1) A body is forced to change its position; it undergoes translation. - 2) A body is forced to change its orientation; it undergoes rotation. - 3) A body is forced to change size; it undergoes dilation. - 4) A body is forced to change shape; it undergoes distortion. These movement components are often described in terms of slip or flow. The distinction is scale- dependent, slip describing movement on a discrete plane, whereas flow is a penetrative movement that involves the whole of the rock. The four basic movements may be combined. - During rigid body deformation, rocks are translated and/or rotated but the original size and shape are preserved. - If instead of moving, the body absorbs some or all the forces, it becomes stressed. The forces then cause particle displacement within the body so that the body changes its shape and/or size; it becomes deformed. Deformation describes the complete transformation from the initial to the final geometry and location of a body. Deformation produces discontinuities in brittle rocks. In ductile rocks, deformation is macroscopically continuous, distributed within the mass of the rock. Instead, brittle deformation essentially involves relative movements between undeformed (but displaced) blocks. Finite strain jpb, 2019 328 Strain describes the non-rigid body deformation, i.e. the amount of movement caused by stresses between parts of a body.
    [Show full text]
  • Introduction to FINITE STRAIN THEORY for CONTINUUM ELASTO
    RED BOX RULES ARE FOR PROOF STAGE ONLY. DELETE BEFORE FINAL PRINTING. WILEY SERIES IN COMPUTATIONAL MECHANICS HASHIGUCHI WILEY SERIES IN COMPUTATIONAL MECHANICS YAMAKAWA Introduction to for to Introduction FINITE STRAIN THEORY for CONTINUUM ELASTO-PLASTICITY CONTINUUM ELASTO-PLASTICITY KOICHI HASHIGUCHI, Kyushu University, Japan Introduction to YUKI YAMAKAWA, Tohoku University, Japan Elasto-plastic deformation is frequently observed in machines and structures, hence its prediction is an important consideration at the design stage. Elasto-plasticity theories will FINITE STRAIN THEORY be increasingly required in the future in response to the development of new and improved industrial technologies. Although various books for elasto-plasticity have been published to date, they focus on infi nitesimal elasto-plastic deformation theory. However, modern computational THEORY STRAIN FINITE for CONTINUUM techniques employ an advanced approach to solve problems in this fi eld and much research has taken place in recent years into fi nite strain elasto-plasticity. This book describes this approach and aims to improve mechanical design techniques in mechanical, civil, structural and aeronautical engineering through the accurate analysis of fi nite elasto-plastic deformation. ELASTO-PLASTICITY Introduction to Finite Strain Theory for Continuum Elasto-Plasticity presents introductory explanations that can be easily understood by readers with only a basic knowledge of elasto-plasticity, showing physical backgrounds of concepts in detail and derivation processes
    [Show full text]
  • Chapter 9 (9.5) – Fluid Pressure
    Chapter 9 (9.5) – Fluid Pressure Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies that are subjected to the action of forces SOLIDS FLUIDS Rigid Bodies TAM 210/211: Statics TAM212: Dynamics Deformable Bodies TAM 251: Solid Mechanics What Makes a Fluid or Solid? Honey Rock What is Sand? Particles swollen with water – ‘Squishy Baff’ Aloe Gel 0 30 60 90 10mm Elastic Increasing force (stress) Viscous They act like a solid… But they flow like a fluid once enough stress is applied. Whipping cream (liquid) + air (gas) = Foam (solid) with compressed air mechanical beating They look like a fluid… Video cornstarch + water = (small, hard particles) But they may bear static loads like solids Summary Water takes shape of its container. Water and rock fit classical definitions of Rock does not. fluid and rock respectively Sand and Squishy Baff take the shape of Sand and Squishy Baff are granular containers, but are composed of solid materials which have properties of both particles fluids and solid The aloe gel holds its shape and can Aloe gel is a suspension of particles trap air bubbles until a certain amount which is able to bear static load like a of stress is applied. solid but behaves like a fluid when “enough” stress is applied. Fluids Pascal’s law: A fluid at rest creates a pressure p at a point that is the same in all directions y For equilibrium of an infinitesimal element, p px F 0:pA cos pA cos 0 p p , x xx x A Fyy0:pA sin pA sin 0 p y p .
    [Show full text]
  • Chapter 15 - Fluid Mechanics Thursday, March 24Th
    Chapter 15 - Fluid Mechanics Thursday, March 24th •Fluids – Static properties • Density and pressure • Hydrostatic equilibrium • Archimedes principle and buoyancy •Fluid Motion • The continuity equation • Bernoulli’s effect •Demonstration, iClicker and example problems Reading: pages 243 to 255 in text book (Chapter 15) Definitions: Density Pressure, ρ , is defined as force per unit area: Mass M ρ = = [Units – kg.m-3] Volume V Definition of mass – 1 kg is the mass of 1 liter (10-3 m3) of pure water. Therefore, density of water given by: Mass 1 kg 3 −3 ρH O = = 3 3 = 10 kg ⋅m 2 Volume 10− m Definitions: Pressure (p ) Pressure, p, is defined as force per unit area: Force F p = = [Units – N.m-2, or Pascal (Pa)] Area A Atmospheric pressure (1 atm.) is equal to 101325 N.m-2. 1 pound per square inch (1 psi) is equal to: 1 psi = 6944 Pa = 0.068 atm 1atm = 14.7 psi Definitions: Pressure (p ) Pressure, p, is defined as force per unit area: Force F p = = [Units – N.m-2, or Pascal (Pa)] Area A Pressure in Fluids Pressure, " p, is defined as force per unit area: # Force F p = = [Units – N.m-2, or Pascal (Pa)] " A8" rea A + $ In the presence of gravity, pressure in a static+ 8" fluid increases with depth. " – This allows an upward pressure force " to balance the downward gravitational force. + " $ – This condition is hydrostatic equilibrium. – Incompressible fluids like liquids have constant density; for them, pressure as a function of depth h is p p gh = 0+ρ p0 = pressure at surface " + Pressure in Fluids Pressure, p, is defined as force per unit area: Force F p = = [Units – N.m-2, or Pascal (Pa)] Area A In the presence of gravity, pressure in a static fluid increases with depth.
    [Show full text]
  • Fluid Mechanics
    I. FLUID MECHANICS I.1 Basic Concepts & Definitions: Fluid Mechanics - Study of fluids at rest, in motion, and the effects of fluids on boundaries. Note: This definition outlines the key topics in the study of fluids: (1) fluid statics (fluids at rest), (2) momentum and energy analyses (fluids in motion), and (3) viscous effects and all sections considering pressure forces (effects of fluids on boundaries). Fluid - A substance which moves and deforms continuously as a result of an applied shear stress. The definition also clearly shows that viscous effects are not considered in the study of fluid statics. Two important properties in the study of fluid mechanics are: Pressure and Velocity These are defined as follows: Pressure - The normal stress on any plane through a fluid element at rest. Key Point: The direction of pressure forces will always be perpendicular to the surface of interest. Velocity - The rate of change of position at a point in a flow field. It is used not only to specify flow field characteristics but also to specify flow rate, momentum, and viscous effects for a fluid in motion. I-1 I.4 Dimensions and Units This text will use both the International System of Units (S.I.) and British Gravitational System (B.G.). A key feature of both is that neither system uses gc. Rather, in both systems the combination of units for mass * acceleration yields the unit of force, i.e. Newton’s second law yields 2 2 S.I. - 1 Newton (N) = 1 kg m/s B.G. - 1 lbf = 1 slug ft/s This will be particularly useful in the following: Concept Expression Units momentum m! V kg/s * m/s = kg m/s2 = N slug/s * ft/s = slug ft/s2 = lbf manometry ρ g h kg/m3*m/s2*m = (kg m/s2)/ m2 =N/m2 slug/ft3*ft/s2*ft = (slug ft/s2)/ft2 = lbf/ft2 dynamic viscosity µ N s /m2 = (kg m/s2) s /m2 = kg/m s lbf s /ft2 = (slug ft/s2) s /ft2 = slug/ft s Key Point: In the B.G.
    [Show full text]
  • Pressure and Fluid Statics
    cen72367_ch03.qxd 10/29/04 2:21 PM Page 65 CHAPTER PRESSURE AND 3 FLUID STATICS his chapter deals with forces applied by fluids at rest or in rigid-body motion. The fluid property responsible for those forces is pressure, OBJECTIVES Twhich is a normal force exerted by a fluid per unit area. We start this When you finish reading this chapter, you chapter with a detailed discussion of pressure, including absolute and gage should be able to pressures, the pressure at a point, the variation of pressure with depth in a I Determine the variation of gravitational field, the manometer, the barometer, and pressure measure- pressure in a fluid at rest ment devices. This is followed by a discussion of the hydrostatic forces I Calculate the forces exerted by a applied on submerged bodies with plane or curved surfaces. We then con- fluid at rest on plane or curved submerged surfaces sider the buoyant force applied by fluids on submerged or floating bodies, and discuss the stability of such bodies. Finally, we apply Newton’s second I Analyze the rigid-body motion of fluids in containers during linear law of motion to a body of fluid in motion that acts as a rigid body and ana- acceleration or rotation lyze the variation of pressure in fluids that undergo linear acceleration and in rotating containers. This chapter makes extensive use of force balances for bodies in static equilibrium, and it will be helpful if the relevant topics from statics are first reviewed. 65 cen72367_ch03.qxd 10/29/04 2:21 PM Page 66 66 FLUID MECHANICS 3–1 I PRESSURE Pressure is defined as a normal force exerted by a fluid per unit area.
    [Show full text]
  • Use of Equations of State and Equation of State Software Packages
    USE OF EQUATIONS OF STATE AND EQUATION OF STATE SOFTWARE PACKAGES Adam G. Hawley Darin L. George Southwest Research Institute 6220 Culebra Road San Antonio, TX 78238 Introduction Peng-Robinson (PR) Determination of fluid properties and phase The Peng-Robison (PR) EOS (Peng and Robinson, conditions of hydrocarbon mixtures is critical 1976) is referred to as a cubic equation of state, for accurate hydrocarbon measurement, because the basic equations can be rewritten as cubic representative sampling, and overall pipeline polynomials in specific volume. The Peng Robison operation. Fluid properties such as EOS is derived from the basic ideal gas law along with other corrections, to account for the behavior of compressibility and density are critical for flow a “real” gas. The Peng Robison EOS is very measurement and determination of the versatile and can be used to determine properties hydrocarbon due point is important to verify such as density, compressibility, and sound speed. that heavier hydrocarbons will not condense out The Peng Robison EOS can also be used to of a gas mixture in changing process conditions. determine phase boundaries and the phase conditions of hydrocarbon mixtures. In the oil and gas industry, equations of state (EOS) are typically used to determine the Soave-Redlich-Kwong (SRK) properties and the phase conditions of hydrocarbon mixtures. Equations of state are The Soave-Redlich-Kwaon (SRK) EOS (Soave, 1972) is a cubic equation of state, similar to the Peng mathematical correlations that relate properties Robison EOS. The main difference between the of hydrocarbons to pressure, temperature, and SRK and Peng Robison EOS is the different sets of fluid composition.
    [Show full text]